0. a 3-D investigation of 2-D organic micro-billiard lasers
Light from the edge:
a 3-D investigation of 2-D organic micro-billiard lasers
Clément Lafargue1, S. Lozenko1 , S. Bittner1, C. Ulysse2, C. Cluzel3, J. Zyss1, M. Lebental1
1 – Laboratoire de Photonique Quantique et Moléculaire, ENS de Cachan.
2 – Laboratoire de Photonique et de Nanostructures , CNRS, Marcoussis.
3 – Laboratoire de mécanique et technologie, ENS de Cachan.
25’’
Joke billiard
Molecular quantum photonics lab

1. Dye-doped polymer micro-cavity
Organic microlasers
Conventional laser
Dye-doped polymer micro-cavity
Amplifying medium +
Resonating
Cavity
Usual configuration
weak confinement
n ≈ 1.5
40’’
Low index = weak confinement, desirable effect
Deep reasons : selection of few orbits,
WGM: Microsphères et microtores de Silice, Cavity quantum electrodynamics group

2. LPQM – microlaser group topics
Chaotic cavities
POSTER, I. Gozhyk :
Towards the control of polarization properties of solid state organic lasers
I. Gozhyk, PRA 86, (2012)
Lebental, APL 88, (2006)
Unidirectional lasing
N.Djellali,
APL 95, (2009)
Emission
Diffraction
Measurement and model
POSTER, S. Bittner :
Localization of modes in a dielectric square resonator
Semi-classical modeling
S.Lozenko
“Microfluid”
EU Project
Analyte solution flow
Numerical modeling
90’’
Interessé/ intrigué par les directions d’émission , on a s’est retrouvé confronté au problème du coin diélectrique.
Mécanisme de sortie -> joue aussi sur la compétition en tre modes vu que pertes=gain
De plus on s’est dit qu’on pouvait peut-être apporter qqchose grâce à nos machins sur le prb même du coin diélectrique

3. Motivation: diffraction at dielectric corners and edges
no solution
Metallic corner
Sommerfeld
1896
30’’
Steady-state
Fil rouge diffraction : expliquer les similitudes et différences des différents cas (diff du FP, dif du carré , diff du triangle-diffractiv orbit)
A standing wave in a resonator to explore the corner

4. Outline Background on organic microlasers Fabrication Experiment
Emission/diffraction properties
Fabry-Pérot like cavities
Square cavities
Triangular microlasers
20’’ 4

5. Outline Background on organic microlasers Fabrication Experiment
Emission /diffraction properties
Fabry-Pérot like cavities
Square cavities
Triangular microlasers
5’’ 5 5

6. Organic microlaser: Fabrication
Cavity n≈1.5
PMMA + Dye
SiO2
n=1.45
n2=1 μm
Fabrication: Electron-beam lithography µm
Microscope photograph
SEM photograph
1μm
0.6 µm µm
Arbitrary cavity shapes
Different laser dyes
40’’ 6 6

7. Organic microlasers: characterization
Excitation geometry
Lasing thresholds
pumping
532 nm
Emission diagrams
~610 nm
emission
collecting lens
Spectrometer
Spectrum L
40’’
Pulsed pumping
Typical spectrum
Images
Wavelength [nm] 7

8. Organic microlasers: characterization
Experimental
Measurements
Lasing thresholds
Emission diagrams
Spectrum L
20’’
Images

9. Organic microlasers: characterization
Experimental
Measurements
Lasing thresholds
FAR FIELD DETECTION
Emission diagrams
Spectrum L
20’’
Dire ‘square’, ‘stadium’
‘sharp lobes’
Images
Physical Review A 75, (2007)

10. Semi-classical approach
Organic microlasers: characterization
Experimental
Measurements
Lasing thresholds
F.S.R.
Emission diagrams
Semi-classical approach
Spectrum L
20’’
FSR linked to the length of PO
Expliquer differentes PO
Images
Periodic Orbits
PRA 76, (2007)

11. Organic microlasers: characterization
Experimental
Measurements
Lasing thresholds
Emission diagrams
Spectrum L
20’’
Images

12. Outline Background on organic microlasers Fabrication Experiment
Emission/diffraction properties
Fabry-Pérot like cavities
Square cavities
Triangular microlasers
10’’ 12 12

13. 3D emission- latitude diagramsFP
Measurement:
50’’
Emission UPLIFTED 13

14. 3D emission- latitude diagramsFP
Sergey Lozenko J.A.P. 111, (2012) z
Measurement: x
50’’
Thin Angular lobes
Free-standing 14

15. 3D emission - latitude diagramsFP
Model: Slit diffraction
Interference (wafer)
50’’
Remind that it is a FP
Enlight the differences
C. Lafargue, to be submitted 15

16. Outline Background on organic microlasers Fabrication Experiment
Emission/diffraction properties
Fabry-Pérot like cavities
Square cavities
Triangular microlasers
20’’ 16 16

17. Square microlaser : diffractive outcoupling
Diamond orbit confined by total internal reflection … nL
= n x 2√2 a
50’’

18. Square microlaser : diffractive outcoupling
Diamond orbit confined by total internal reflection …
… but losses occur via diffraction
30’’ 18

19. Square microlaser : diffractive outcoupling
Pump :
30’’
+ example pola effect
Camera
Pump polarization effects
I. Gozhyk, PRA 86, (2012),

20. Square microlaser : diffractive outcoupling
The diffraction at the corners here is not at all understood, but it would be important to do so
the latitude diagrams depend strongly on the kind of mode inside the resonator -> maybe there is some kind of connection between the diffraction in the two different directions.

21. Outline Background on organic microlasers Fabrication Experiment
Emission/diffraction properties
Fabry-Pérot like cavities
Square cavities
Triangular microlasers
20’’ 21 21

22. Periodic Orbits in triangles
A not so simple shape (not regular contour)
No totally confined periodic orbits
An open mathematical question: 
«  Does a periodic orbit in a triangle exist ? »
Alain Grigis, University Paris XIII ?

23. FP winning
100°
40°

24. FP not always winning Camera view 110° 35° 35° 110°
Despite the fact FP is in family, the other isolated orbit is winning

25. Diffractive orbit
98.04°
40°
41.96°
« DO not exist in classical mechanics »

26. Summary Diffraction effects from the edges on different contours :
3D Fabry-Pérot emission well understood
Square : emission at the corners
3D emission depends on the cavity shape
Triangles
Identification of orbits
Switching between different types of orbits
Observation of a diffractive orbit

27. Perspectives
5’’

29. 110°
110°
700

30. phi= 60°
phi= -22°
Incidence 0°
Incidence 40°

31. Does a periodic orbit in a triangle exist ?
Alain Grigis, University Paris XIII
Acute triangles
feet of the altitudes
Less than 100° triangles:
Journal of Experimental Mathematics, 18, p. 137 (2008)
Rational triangles : angles = pp/m , unfolding theory
Others … 31

32. Information in the laser spectrum : Length L of the periodic orbit
Semi-Classical point of view
Information in the laser spectrum : Length L of the periodic orbit
Lasing L n1 n2 32 32

33. Periodic orbits & trace formula
Density of states
Wave physics
Semi-classical limit
Classical physics
PRE 83, (2011)
Sum on
periodic
orbits
Length
of the
orbits
Fresnel
reflexion
coefficients
Coeff depending only on classical quantities

34. Effective index approximation
Electromagnetism z
Passive cavity (no laser) :
resonances
w ?
Boundary conditions
Outside
Inside
(Dxy + neff ² k²) z
Effective index approximation 34

35. From electromagnetism to wave chaos
2D problem
Boundary conditions
diffraction 35

36. Resonance computation
Square: not integrable
Diamond
-1.2
100
Charles Schmit, Eugène Bogomolny
Phys. Rev. E 83, (2011) 36

37. How to fabricate ?
What are the emission directions ?

38. 3D – Polarization selectionq q
Pump polarization
Camera 38

39. 3D – Polarization selection
Pump polarization :
(Camera) 39